91Ó°ÊÓ

Absolute value describes the distance from zero that a number is on the number line,without considering direction. The absolute value of a number is never negative.

Consider the expression $|a-3|-14=-6$.

Add 14 on both sides of the equation as follows:

$\begin{array}{l}|a−3|−14=−6\\ |a−3|−14+14=−6+14\\ |a−3|=8\end{array}$

Apply the absolute rule as follows:

Case 1. When $a-3=8$.

$\begin{array}{l}a−3=8\\ a=8+3\\ a=11\end{array}$

Case 2. When $a-3=-8$

$\begin{array}{l}a−3=−8\\ a=−8+3\\ a=−5\end{array}$

Therefore, the value is $a=11,-5$.

Substitute $a=11,-5$in the equation $|a-3|-14=-6$and simplify as follows:

$\begin{array}{l}|a−3|−14=−6\\ |11−3|−14=−6\\ \left|8\right|−14=−6\\ 8−14=−6\\ −6=−6\end{array}$

$\begin{array}{l}|a−3|−14=−6\\ |−5−3|−14=−6\\ |−8|−14=−6\\ 8−14=−6\\ −6=−6\end{array}$

Since the left-hand side and right-hand side is equal in both the cases thus the values are$a=11,-5$.